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Periodic solutions of a non-autonomous predator–prey system with migrating prey and disease infection: via Mawhin’s coincidence degree theory

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Abstract

In this paper, we consider a non-autonomous competitive predator–prey system with migrating prey and disease infection in both species. Based on some novel estimation techniques for the prior bound and Mawhin’s coincidence degree theorem, some sufficient conditions for the permanence and existence of periodic solutions are obtained. A suitable Lyapunov function was constructed to prove the global asymptotical stability of the positive periodic solution. Finally, an example and its numerical simulations demonstrate the validity of the results.

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Acknowledgements

This work was jointly supported by the National Natural Science Foundation of China under Grant (Nos. 11671176 and 11871251), Natural Science Foundation of Fujian Province under Grant (No. 2018J01001), start-up fund of Huaqiao university (Z16J0039), Fujian Province Young Middle-Aged teachers education scientific research project (No. JT180558 ). The authors thank the editor and anonymous referees for their valuable suggestions and comments, which improved the presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics and Computer, Wuyi University, Wu Yishan, 354300, Fujian, People’s Republic of China

    Hang Zheng & Lei Guo

  2. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, People’s Republic of China

    Yuzhen Bai

  3. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yonghui Xia

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  1. Hang Zheng
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  2. Lei Guo
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  3. Yuzhen Bai
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  4. Yonghui Xia
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Contributions

HZ carried out the computations and figures in the proof. YX conceived of the study, designed, drafted and finished the manuscript. The other authors participated in the discussion of the project. All authors read and approved the final manuscript.

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Correspondence to Yonghui Xia.

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Zheng, H., Guo, L., Bai, Y. et al. Periodic solutions of a non-autonomous predator–prey system with migrating prey and disease infection: via Mawhin’s coincidence degree theory. J. Fixed Point Theory Appl. 21, 37 (2019). https://doi.org/10.1007/s11784-019-0674-2

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